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Non-adaptive hypergeometric group testing. (English) Zbl 0639.62076
Summary: In a hypergeometric group testing problem we have a set of n items known to contain exactly d defectives. The problem is to identify all the defectives through group testing with a minimal number of tests where a test consists of a specified subset of the items and has the outcome pure if none of the items in the subset is defective and the outcome contaminated otherwise. A testing procedure is called non-adaptive if all tests have to be specified simultaneously. We translate this group testing problem into an extremal problem for set-systems and give estimates for the size of the extremal systems.

62K99 Design of statistical experiments
62P30 Applications of statistics in engineering and industry; control charts
05A05 Permutations, words, matrices